Final answer:
To find the resistance, calculate the power dissipated using the formula P = E / t, and then use the power formula P = V^2 / R with the given voltage (9.0 V) to solve for R, which is approximately 10.42 ohms.
Step-by-step explanation:
The question involves calculating the resistance of a resistor in an electrical circuit, using the provided information about the voltage, energy, and time. To find the resistance, one must first determine the power dissipation using the formula P = É / t, where E is the energy (1.4×105 J) and t is the time (5.0 hours). Then, power can be expressed as P = V^2 / R, allowing us to solve for R, the resistance, using the given voltage (9.0 V).
First, calculate the power dissipated by the resistor:
P = (1.4×105 J) / (5.0 hours × 3600 seconds/hour) = 7.778 W (rounded to three significant figures).
Next, rearrange the power formula to solve for resistance:
R = V^2 / P = (9.0 V)^2 / 7.778 W = 10.42 Ω